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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold networks

We propose the artificial intelligence velocimetry-thermometry (AIVT) method to reconstruct a continuous and differentiable representation of the temperature and velocity in turbulent convection from measured three-dimensional (3D) velocity data. AIVT is based on physics-informed Kolmogorov-Arnold networks and trained by optimizing a loss function that minimizes residuals of the velocity data, boundary conditions, and governing equations. We apply AIVT to a set of simultaneously measured 3D temperature and velocity data of Rayleigh-Bénard convection, obtained by combining particle image thermometry and Lagrangian particle tracking. This enables us to directly compare machine learning results to true volumetric, simultaneous temperature and velocity measurements. We demonstrate that AIVT can reconstruct and infer continuous, instantaneous velocity and temperature fields and their gradients from sparse experimental data at a high resolution, providing an additional approach for understanding thermal turbulence.

Science & Technology - Other Topics↗
DOE OSTI2026

Joint scheduling of energy, fast and primary frequency response reserves in integrated transmission–distribution networks

Inverter-based distributed energy resources (DERs) connected to distribution networks (DNs) can provide fast frequency support, but their reserve deliverability depends on feeder constraints and differs from synchronous primary frequency response (PFR). Existing transmission–distribution coordination studies usually treat reserve generically or neglect feeder-level feasibility, while frequency-security scheduling studies rarely represent distribution feeders explicitly. This paper develops a bi-level day-ahead scheduling framework for integrated transmission–distribution networks that jointly clears energy, transmission-side PFR, and distribution-side fast frequency response (FFR) under exogenous hourly inertia and largest-loss inputs from an external unit commitment (UC) schedule. The transmission problem is modeled with DC-optimal power flow (OPF) and closed-form second-order cone (SOC) frequency-security constraints, whereas each DN is represented by a reserve-aware branch-flow AC-OPF so that scheduled fast reserves remain deliverable during activation. The bi-level problem is reformulated through Karush–Kuhn–Tucker (KKT) conditions into a mixed-integer SOC program, and a penalty term is used to tighten the distribution-network relaxation. In the reduced test system, lower exogenous inertia increased the required primary response from 179.64 MW to 191.08 MW, distribution-side fast response reduced total frequency-response procurement by up to 4.9%, and neglecting distribution constraints overstated the combined distribution-side energy and reserve award by up to 18%. In the expanded study, the largest case was solved in 2.02 s with a 0.00% optimality gap. Time-domain simulations kept the frequency nadir above 59.0 Hz in all tested hours. These results demonstrate the value of fast-response modeling and distribution-feasible reserve delivery in coordinated market clearing.

Noh, Seung-Gil↗
DOE OSTI2025

Active Fluids Form System-Spanning Filamentary Networks

Recent experimental realizations of liquid-liquid phase separation of active liquid crystals have offered an insight into the interaction between phase separation, ubiquitous in soft matter and biology, and chaotic active flows. Here, in this Letter, we use continuum theory to examine phase separation of an active liquid crystal and a passive fluid and report two new results. First, we provide an analytical derivation of the activity-induced suppression of the phase boundary of the coexistence region—a result first reported in simulations and experiments. We show that the shift in the critical point is a result of the balance between self-stirring active flows and phase-separating diffusive fluxes. Second, we show that this same balance is responsible for dramatically changing the morphology of the phase separated state, resulting in the emergence of a new mixed active phase consisting of a dynamical filamentous active network that invades the entire system area, trapping droplets of passive material. This structure exists even for very low volume fractions of active material. Our work provides an important step towards the goal of understanding how to use activity as a new handle for sculpting interfaces.

active nematics↗
DOE OSTI2025

A Novel Protection Scheme for Unbalanced Faults in Inverter Dominated Networks: A Computationally Efficient Algorithm for Entry-Level Relays

Microgrids are now a common practice in distribution systems to increase resilience and reliability. However, microgrid protection remains a critical challenge, considering its requirement to operate in both grid connected and islanded, and the variability in fault characteristics under each mode of operation. This paper presents unbalanced power (S unb ) based fault detection algorithm, which considers local voltage and current unbalances to determine faults in the system. S unb is a computationally efficient fault detection algorithm that is suitable for implementation in the programmable logic of entry level protective relays. In addition, the difference in current and voltage unbalance (D n ) is used to determine the fault type. The proposed method demonstrates high sensitivity and selectivity for line-to-ground (LG), line-to-line (LL), and double line-to-ground (LLG) faults, representing the most common faults in distribution systems. It also allows relay coordination with upstream and downstream protection devices in both island and grid connected operation, while preserving grading margins. The same pickup and time multiplier settings of a particular relay for both modes of operation eliminates the need for adaptive settings, which rely on communication networks. Validation was performed with a hardware-in-the-loop (HIL) setup using Typhoon HIL real time simulator interfaced with three entry-level, SEL 751 relays. Results confirmed the algorithm’s ability to discriminate fault conditions, and determine the fault type under both operating modes, maintain fast detection times, and ensure proper protection coordination.

fault classification↗
DOE OSTI2026

SODAs: sparse optimization for the discovery of differential and algebraic equations

Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by time-scale separation, conservation laws and physical constraints. While sparse optimization has revolutionized model development by allowing data-driven discovery of parsimonious models from a library of possible equations, existing approaches for dynamical systems assume DAEs can be reduced to ODEs by eliminating variables before model discovery. This assumption limits the applicability of such methods for DAE systems with unknown constraints and time scales. We introduce sparse optimization for differential-algebraic systems (SODAs), a data-driven method for the identification of DAEs in their explicit form. By discovering the algebraic and dynamic components sequentially without prior identification of the algebraic variables, this approach leads to a sequence of convex optimization problems. It has the advantage of discovering interpretable models that preserve the structure of the underlying physical system. To this end, SODAs improves since SODAs is singular numerical stability when handling high correlations between library terms, caused by near-perfect algebraic relationships, by iteratively refining the conditioning of the candidate library. We demonstrate the performance of our method on biological, mechanical and electrical systems, showcasing its robustness to noise in both simulated time series and real-time experimental data.

DAE↗
DOE OSTI2026

Entropy-defect synergy for dual luminescence mechanism in spinel: Time-resolved anti-counterfeiting and fingerprint visualization

Multimodal luminescent materials, while promising for anti-counterfeiting, often lack dynamic time-dependent responses and controllable spatial distribution, limiting their encryption capabilities in the spatiotemporal dimension. Here, this work presents a coordinated control strategy based on entropy and defect engineering, and uses a backpropagation (BP) neural network for material screening to successfully prepare spinel Mg 0.8 (Fe 0.04 Co 0.04 Ni 0.04 Cu 0.04 Zn 0.04 )Cr 2 O 4 (MgA 5 CO) phosphors with time-dependent dynamic luminescence behavior. This phosphor simultaneously activated the d-d transition luminescence (∼618 nm) derived from Co 2+ /Cr 3+ and the defect luminescence (∼398 nm) related to zinc vacancies (V Zn ) in a single-phase solid solution. The phosphor exhibits a time-dependent color evolution from pink to purple under fixed-wavelength excitation, due to the different excited-state dynamics and decay lifetimes associated with the d-d transition and defect luminescence. Structural characterization and spectral analysis confirmed the existence of V Zn and its significant role in defect luminescence process. The fluorescent and dynamic luminescent properties of entropy-based spinel oxide enable its use in advanced anti-counterfeiting applications like fingerprint recognition and color-changing dedicated anti-counterfeiting mark, showing promise in high-end and time-dynamic anti-counterfeiting fields. This research not only developed a new type of fluorescent dynamic anti-counterfeiting material, but also provided a new idea for constructing advanced optical functional materials with multiple luminescence mechanisms.

Defect project↗
DOE OSTI2026

Dynamic Diketoenamine Crosslinking Unlocks Vinyl Polymer Vitrimers From β ‐Triketone Chemistry

Covalent adaptable networks (CANs) offer a compelling strategy to unite the mechanical robustness of thermosets with the reprocessability of thermoplastics, yet achieving simultaneous durability, processability, and true recyclability remains challenging. We introduce diketoenamine (DKE) vitrimers derived from β-triketone methacrylate monomers and demonstrate how rational monomer design dictates network processability, viscoelasticity, and recyclability. By systematically varying the spacer length between the β-triketone (TK) moiety and the polymer backbone, we identify a key structure–property relationship that dictates vitrimer behavior. Networks bearing TK pendants minimally displaced from the backbone suppress creep but exhibit limited stress relaxation, whereas extended spacers yield lower glass transition temperatures, higher effective crosslink densities, and efficient stress dissipation, enabling optical transparency and reprocessability. Extending this platform to ultra-high molecular-weight prepolymers introduces physical entanglements as secondary crosslinks, further enhancing dimensional stability without compromising processability. Both mechanical and chemical recycling validate the closed-loop circularity of these materials. Furthermore, these results establish TK methacrylates as a versatile platform for designing high-performance vitrimers that integrate durability, reprocessability, and true closed-loop recyclability.

closed-loop recyclability↗
DOE OSTI2026

Coalition for Community-Supported Affordable Geothermal Energy Systems (C2SAGES)

The C2SAGES project evaluated the feasibility of a community geothermal system for the planned Windy Ridge affordable housing development in Hinesburg, Vermont. Led by GTI Energy with Vermont Gas Systems, LN Consulting, NREL, and Frontier Energy, the work assessed technical design, energy performance, costs, business models, community engagement, maintenance, workforce development, and permitting. The proposed system was designed to serve 100% of the development’s heating, cooling, and domestic hot water loads. Compared with a baseline using air-source heat pumps and natural gas water heating, the geothermal system was estimated to reduce HVAC and domestic hot water energy use by about 45% to 48%, lower operating and maintenance costs, and reduce 30-year life-cycle costs by 37% for Phase 1 and 10% for Phase 2. Technical testing and modeling indicated that the Windy Ridge site is suitable for a community-scale geothermal system. The project also developed borehole field layouts, piping concepts, pump house designs, controls, maintenance plans, and supporting engineering drawings. The business model analysis found that first cost, ownership structure, and customer affordability remain major deployment challenges. Utility-led maintenance and operation were viewed favorably, but traditional utility cost-recovery models may require subsidy or revised financing structures to be practical for affordable housing. Community engagement highlighted the need for clear public education, transparent financing, reliable long-term maintenance, trained technicians, and the potential to pair geothermal systems with weatherization. Overall, the report concludes that community geothermal is technically feasible and offers meaningful energy, emissions, and life-cycle cost benefits, but broader deployment will depend on workable financing models and workforce readiness.

15 GEOTHERMAL ENERGY↗
DOE OSTI2027

From zonal to nodal capacity expansion planning: Spatial aggregation impacts on a realistic test-case

Solving power system capacity expansion planning (CEP) problems at realistic spatial resolutions is computationally challenging. Thus, a common practice is to solve CEP over zonal models with low spatial resolution rather than over full-scale nodal power networks. Due to improvements in solving large-scale stochastic mixed integer programs, these computational limitations are becoming less relevant, and the assumption that zonal models are realistic and useful approximations of nodal CEP is worth revisiting. Here, this work is the first to conduct a systematic computational study on the assumption that spatial aggregation can reasonably be used for ISO-scale CEP. By considering a realistic, large-scale test network based on the state of California with over 8000 buses, we find that well-designed small spatial aggregations can yield good approximations but that coarser zonal models may result in large distortions of investment decisions, e.g., capacity under-investment of up to 41% for the lowest resolution model considered.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1984

The Telecommunications and Data Acquisition Report

Tracking and ground-based navigation; communications, spacecraft-ground; station control and system technology; capabilities for new projects; networks consolidation program; and network sustaining are described.

E C Posner↗
DOE OSTI2015

Crossover from quantum to classical transport

Understanding the crossover from quantum to classical transport phenomena has become of fundamental importance not only for technological applications due to the creation of sub-10nm transistors – an important building block of our modern life – but also for elucidating the role played by quantum mechanics in the evolutionary fitness of biological complexes. This article provides a basic introduction into the nature of charge and energy transport in the quantum and classical regimes. Here, it will identify the characteristic transport properties in both limits, and demonstrate how they can be connected through the loss of quantum mechanical coherence. I will identify the salient features of the crossover physics, and demonstrate their importance in opening new transport regimes and for understanding efficient and robust energy transport in biological complexes.

charge↗
DOE OSTI2026

Thermal Reservoir Networks for Modularly Expandable Thermal Microgrids

The Department of Defense (DoD) faces the substantial challenge of cost-effectively retrofitting one to two installations per month, each comprising approximately 1,000 buildings, to improve resilience, reduce energy consumption, and enhance energy supply security. Achieving these objectives requires optimal system selection and effective risk mitigation during system integration. To address this need, we introduce Platform-Based Design (PBD), a structured, hierarchical methodology adapted from other industrial sectors to the domain of energy system retrofits. We demonstrate the effectiveness of PBD through a techno-economic feasibility study comparing geothermal-coupled thermal energy networks (TENs) with conventional energy systems for heating, cooling, and powering 17 buildings at Joint Base Andrews (JBA) in Maryland. Our analysis illustrates that the PBD approach enables rigorous, data-driven, sequential decision making, resulting in a family of Pareto-optimal systems, among which the TEN emerged as the most promising solution. The selected TEN design integrates geothermal borefields, heat recovery heat pumps, photovoltaic (PV) arrays, and battery storage. Compared to the baseline system – gas heating combined with air-source chillers – the proposed TEN reduces annual imported energy by 74% and peak electricity demand by 45%, achieves a levelized cost of energy of $\$0.210$/kWh, and substantially enhances resilience. Life-cycle costs increase by approximately 6%, and initial investment costs are about 2.5 times higher than the baseline. However, if central plant infrastructure, district loops, and utility-scale PV and battery systems are privately funded and operated, the initial investment would fall below the baseline system cost. Critical to achieving these significant performance improvements were detailed nonlinear dynamic simulations coupling geothermal heat transfer, energy system operation, and realistic feedback control logic. These simulations identified essential design modifications and control strategy refinements that substantially reduced energy use, peak demand, and compressor shortcycling, thereby improving durability and reliability—issues that would have been significantly more expensive to resolve during operation. Additionally, the verification step highlighted sensitivities to key design parameters that could reduce initial investment by approximately $\$2$ million and reduce annual life-cycle costs more than $\$300,000$. We recommend adopting the PBD methodology for future feasibility studies and TEN pilot projects to gain valuable operational experience. Furthermore, we recommend that DoD invest in transferring and scaling the PBD methodology to other installations. This entails developing standardized computational frameworks and component libraries as well as training industry in conducting PBD. Such investments would enable rapid, robust, reliable, and cost-effective retrofits, supporting DoD’s ambitious energy system modernization goals.

Wetter, Michael [Lawrence Berkeley National Labora↗
DOE OSTI2026

Lunar accelerometer network gravitational observatory (LANGO)

With ground-based interferometers detecting hundreds of gravitational-wave (GW) events, GW astronomy has continued to blossom. U.S. and European scientists are developing plans to construct third-generation ground-based interferometers. ESA has proceeded through the mission formulation phase of space-based interferometer in a lower-frequency band, 10 –4 –0.1 Hz. Despite all these exciting developments, there is still a missing frequency band, 0.1–10 Hz. This mid-frequency band is rich with interesting astrophysical events. Coalescence and merger of intermediate-mass black holes (IMBHs) will occur in this frequency band. Coalescing stellar-mass BHs will pass through this frequency band days before they reach the frequency band of LIGO and Virgo. Detection of such signals would enable a mid-frequency detector to issue an advance notice to the high-frequency GW detectors, as well as to optical, x-ray and γ-ray telescopes. We propose Lunar Accelerometer Network Gravitational Observatory (LANGO) to detect GWs in this frequency band. In the first phase (LANGO 1), we propose to deploy four ambient-temperature (250 K) accelerometers in the tetrahedral or in a square configuration on the hemisphere facing the Earth. After successful operation at 250 K, LANGO would be upgraded to a cryogenic (4 K) version with over two orders of magnitude increased sensitivity (LANGO 2), with coherent rejection of seismic noise implemented. LANGO is a full-tensor detector, capable of determining the source direction and wave polarization. Each test mass (TM) is suspended as a pendulum with resonance frequency ∼ 0.01 Hz, thus is only weakly coupled to the lunar surface horizontally. LANGO is designed to detect the relative motion of globally separated, nearly free, TMs by using the Moon as a large quiet platform. LANGO 1 and 2 accelerometers aim at sensitivities ⩽ 10 –11 m s –2 Hz –1/2 and ⩽ 10 –13 m s –2 Hz –1/2 in the horizontal axes over the frequency band of 1 mHz–10 Hz, which yield GW sensitivities 1.1 x 10 -21 Hz -1/2 and 3.8 x 10 -24 Hz -1/2 at 1 Hz, respectively. The LANGO accelerometers will be 10 3 –10 5 times more sensitive than Apollo seismometers. With such sensitivity, LANGO will also make great contribution to the advancement of lunar geophysics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Correlated Ion Transport Governed by Dynamic Local Structure in High Concentration and Localized High Concentration Electrolytes

Understanding the dynamics of cluster formation and network percolation provides the mechanistic link between microscopic solvation structure and transport in concentrated electrolytes, including localized high-concentration electrolytes (LHCEs). Although recent studies have shown LHCEs to form micelle-like aggregates at specific compositions, a quantitative understanding of how solvation structures and transport properties depend on salt–solvent–diluent ratios remains limited. Here, we integrate molecular dynamics with Onsager transport analyses to chart the evolution of solvation microstructure and associated ionic transport in LiFSI/DMC/TTE, achieving good agreement with experimental conductivities across composition. We show that micelle formation arises from a dynamic instability of the cation–anion network, and that network percolation is the primary determinant of conductivity. Two compositional thresholds emerge: A critical network concentration (CNC) and a critical micelle concentration (CMC) that delineate transitions from extended percolating networks to micelle-like clusters and then to fragments. These structural transitions rationalize the nonintuitive conductivity decrease at intermediate dilution despite monotonically decreasing viscosity and provide composition-level design rules for LHCEs.

Mohanakrishnan, Rohith Srinivaas [University of Ca↗
NASA NTRSDate not supplied

Enabling Interoperability in Earth System Digital Twins (ESDT): Integrating Observations, Models, and AI for Actionable Insights Through NASA'S Intelligent Systems Technology Program

NASA’s Intelligent Systems Technology Program (IST) is driving a paradigm shift in Earth science through the development of Earth System Digital Twins (ESDT). These integrated information systems create a dynamic "digital replica" of the Earth by harmonizing continuous, multi-source observations with high-fidelity models and state-of-the-art artificial intelligence (AI) that enable “What now?”, “What next?”, and “What if?” scenario building. These scenarios are reflected in NASA IST’s series of ESDTs, from the Coastal Zone Digital Twin that integrates complex data on the current state of the Chesapeake Bay to the Terrestrial Environmental Rapid-Replication and Assimilation Hydrometeorological (TerraHydro) AI-based ESDT that forecasts water movement across Earth’s surface, to the Agriculture Land Information System (AgLIS) which can be used to assess optimal planting dates and crop yield estimates. By bridging the gap between vast data archives and actionable insights, these projects enable a system-of-systems approach to understanding complex, interacting Earth processes. This poster will highlight recent innovations and future directions from NASA’s ESDT initiatives: Continuous Data Assimilation & Multi-Source Fusion. A core requirement of the ESDT work is the transition from static models to dynamic "living" replicas. This involves creating frameworks for the continual assimilation of near-real-time data from uncoordinated, heterogeneous sources, including satellite observations and airborne assets, and ground-based Internet of Things (IoT) sensors. These systems link design, operational status, and environmental data, ensuring the digital twin accurately reflects the current state of the physical Earth system. High-Fidelity Hybrid Modeling & Computational Acceleration to enable interactive "what-if" explorations, programs are moving beyond traditional, slow physical solvers by developing fast surrogate machine learning models and Deep Generative Models (DGMs). These hybrid approaches use neural networks to emulate complex physics, such as cloud feedback or ocean dynamics, at a fraction of the original computing cost, often leveraging advanced hardware like Graphics Processing Units (GPUs) to achieve the necessary scale. Federated Ecosystems & Interoperable Frameworks rather than building isolated tools, NASA IST is moving toward federated ESDTs and reusable analytic collaborative frameworks. This theme focuses on interoperability standards and common ontologies that allow specialized digital twins to interact and share data. This system-of-systems architecture supports multi-discipline investigations, such as analyzing how upstream watershed changes impact downstream urban flooding or how wildfire emissions affect regional air quality. By leveraging these advancements, ESDTs empower researchers and decision-makers to conduct real-time analysis and run complex hypothetical scenarios, ultimately improving our understanding of Earth’s evolving systems and informing critical real-world applications.

Earth System↗
DOE OSTI2025

Complex-Valued Intermolecular Coupling Enables Directional Exciton Transport in Excitonic Circuits

Molecular systems capable of directing the flow of excitons are key to the development and optimization of optoelectronic materials. The transport of excitons across multiple molecules is governed by an intermolecular electronic coupling network. In this article, we consider the effects of complex-valued intermolecular electronic coupling on exciton transport. Here, we present a molecular motif capable of generating complex-valued coupling under excitation with circularly polarized light. We use theoretical modeling and simulation to illustrate how complex coupling can be leveraged to drive the rotational flux of excitons in cyclic molecular networks and direct the exciton population in branched molecular networks.

chromophores↗
DOE OSTI2024

Autonomous phototaxis of hydrogel swimmers

The design of synthetic soft matter capable of emulating the complex behaviors of living organisms, such as sensing and adapting to their environment, remains an important challenge in developing biomimetic materials. Functionalized hydrogels are ideal candidates for such materials since they are highly responsive to their environment and can be operated in water. In this work, we investigate a hybrid bonding hydrogel composed of peptide amphiphile supramolecular nanofibers covalently attached to a photoresponsive network, in which high-aspect-ratio ferromagnetic nanowires are aligned along the length of the sample, designed to swim under oscillating magnetic fields. This hybrid hydrogel swimmer can autonomously swim toward a light source by utilizing photoinduced interactions between supramolecular and covalent networks reminiscent of phototactic swimming in living systems. Using a combination of experimental techniques and a continuum model incorporating photochemistry, magnetoelasticity, and hydrodynamics, we explain the swimming mechanism and predict phototactic behavior. Our work highlights the potential role of hybrid bonding polymers, which leverage the interplay between supramolecular assemblies and covalent networks. We demonstrate how these polymers can be tailored to react dynamically to their environment, paving the way for developing intelligent and autonomous robotic systems.

Science & Technology - Other Topics↗
DOE OSTI2026

Passive Confirmation of the Presence Of High-Explosive Material Via Neutron Transmission Spectroscopy

The goal of this project was to explore a novel approach for identifying presence and potential types of high explosives (HE) in treaty-controlled items with passive neutron sources by using passive neutron transmission spectroscopy. We predominantly look to measure relative elemental abundance of Carbon, Hydrogen, Oxygen, and Nitrogen (CHON) since most relevant materials are certain mix of these elements, as shown in Table 1. Previously, most studies exploring potential identification of CHON elemental content of targets in the vicinity of passive neutron source were focused solely on gamma spectroscopy using high resolution gamma detectors. Using neutron transmission spectroscopy with pulse-shape discrimination (PSD) capable organic scintillators is not only a novel idea in of itself, but arguably necessary for accurate identification of the CHON elemental content of an interrogated target. While high resolution gamma spectroscopy in principle can determine a presence of hydrogen and nitrogen, it is effectively blind to a quantitatively measuring areal densities of C, O. The initially proposed approach, described in detail in the project proposal, was to leverage previous Monte Carlo study on neutron transmission spectroscopy using slab shaped target interrogated with well-collimated (“pencil”) neutron beam. In this study, a simulated test CO 2 target was interrogated by a pencil neutron beam and transmitted neutron spectra were measured using PSD capable organic scintillator using MLEM based unfolding technique. To establish relative elemental content of carbon and oxygen, the unfolded neutron spectrum was fit with a parametrized combination of their respective elemental spectral templates. The individual spectral template was calculated by convoluting ENDF neutron crosssection with the known resolution of the PSD detector used in the study. This approach in the studied configuration successfully quantitatively established relative elemental composition of carbon and oxygen.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗